Coal is carried from a mine in West Virginia to a power plant in
New York in hopper cars on a long train. The automatic hopper car
loader is set to put 62 tons of coal into each car. The actual
weights of coal loaded into each car are *normally
distributed*, with mean *μ* = 62 tons and standard
deviation *σ* = 1.2 ton.

(a) What is the probability that one car chosen at random will
have less than 61.5 tons of coal? (Round your answer to four
decimal places.)

(b) What is the probability that 31 cars chosen at random will have
a mean load weight *x* of less than 61.5 tons of coal?
(Round your answer to four decimal places.)

(c) Suppose the weight of coal in one car was less than 61.5 tons.
Would that fact make you suspect that the loader had slipped out of
adjustment?

Yes

No

Suppose the weight of coal in 31 cars selected at random had an
average *x* of less than 61.5 tons. Would that fact make you
suspect that the loader had slipped out of adjustment? Why?

Yes, the probability that this deviation is random is very
small.

Yes, the probability that this deviation is random is very large.

No, the probability that this deviation is random is very small

No, the probability that this deviation is random is very large.

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